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Math Help - Dynamical systems

  1. #1
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    Dynamical systems

    Suppose that y' = ay - H y(0) = y0, models a fish population where a and H are positive constants and 0 <y0 < H/a. Find the time t* when the population dies out. [Hint: set y = 0 in solution formula (9) and solve for t.]

    The solution formula, which I have confirmed both algebraically and through the answer book, is y = y0e^[at]

    How can I solve for t in this problem when y = 0? e^[at] never reaches zero. The only way I know to do this is to make y0 = 0. That does not solve for t, however.

    The hint aside, I thought I would look for ways to make y' (the rate) = 0.
    Therefore, y=H/a.

    Where am I going wrong?

    Thanks!
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    Hi there, I get a solution to the D.E. as

    \displaystyle y(t) = y_0 e^{at}-\frac{H}{a} e^{at}+\frac{H}{a}
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